Basic Descriptive Statistics: Measures of Variation


  Date: 2024
  License: CC BY-NC-SA
  Domain: Processing Data
  Subdomain: Analyzing Data
  Type of Resource: Lesson Plan

Phenomena in the world vary, and statistical analysis provides powerful tools for describing this variability and for understanding what such variation means. Understanding how phenomena vary–or remain stable–can be a first step towards identifying how social pressures or power differentials might be impacting observed realities. This lesson plan provides a set of activities to introduce students to basic tools for measuring and understanding variation in data.

Keywords:  descriptive statistics    measures of variation    statistical analysis  


Instructor Note:

This lesson can be paired with the “Basic Descriptive Statistics: Measures of Central Tendency” activity in this Data Advocacy Toolkit.

Learning Goals

Develop basic tools for describing variation within a dataset Provide practice calculating various measure of variation

Readings

Matthew J.C. Crump, Answering Questions With Data, chapters 2.5-2.5.4, Shafer and Zhang, Introductory Statistics, “2.3: Measure of Variability” and “2.4: Relative Position of Data”

Agenda

Discussing Key Concepts (15 minutes) Exploring Variation (30 minutes) Assessing Variation in a Dataset (30 minutes)

Activities

Discussing Key Concepts (15 minutes)

Use this time to check in with students about the concepts covered so far in the module and to discuss the terms covered in the readings for today’s class. Have students summarize in their own words the lessons of the past two class periods, inviting them to identify any points of confusion they might have about the material covered thus far in the module. Have them define the following terms and come up with a concrete example of the concept in action:

  • Range
  • Interquartile range
  • Variance
  • Standard deviation

Exploring Variation (30 minutes)

This activity builds on the lesson plan also included in the Data Advocacy Toolkit, “Basic Descriptive Statistics: Measures of Central Tendency.” Utilizing the same data students generated in that lesson plan’s second exercise and utilizing the calculated mean of the student-generated data, have students perform the following tasks by hand, creating a chart of their calculations (as in the Crump reading) and using a calculator where necessary:

  • Identify the range of the dataset by locating the maximum and minimum values
  • Calculate the difference score for each observation by subtracting the mean value from each observation.
  • Calculate the variance for the data by squaring each observation, adding up the total of these squares and then divide that total by the total number of observations.
  • Now calculate the standard deviation by calculating the square root of the variance
  • What does the standard deviation tell you? What kind of conclusions can you draw about your dataset based on the data you’ve generated across the two class meetings?
  • The exercise has asked you to calculate data based on the population of students in your class. Could the information you’ve gathered be taken as a representative sample of the student body in your institution as a whole? Why or why not?

Assessing Variation in a Dataset (30 minutes)

This exercise asks students to explore a Gapminder dataset that focuses on the percentage of total energy use in a given country that derives from renewable energy sources (link).
Using the software platform of your choice, have the students calculate:

  • Mean and median scores for a given year
  • Range
  • Which country had the highest percentage usage of renewable energy in 1990? In 2019?
  • Which country had the lowest percentage usage of renewable energy in 1990? In 2019?
  • Interquartile range for any year
  • Standard deviation for any year
  • Given the mean and median scores and the standard deviation, what can you say about the data?
  • What do the measures calculated above tell us about how the United States is positioned in the world with respect to renewable energy usage? If time, have students pick a country and calculate the measures above for one country.